Derivation of the probability rule

A derivation of the rule that states that ψ^*(x̅ )ψ(x̅ ) is the coordinate probability distribution at the space-time point x̅ in quantum mechanics is presented. A coordinate-measuring experiment involving two light pulses that overlap at a prescribed space-time point is employed. A classical charged particle would reveal itself by absorbing energy from each pulse and reemitting a light wave whose energy and direction can be measured. In order to repeat this experiment a large number of times, the wave function must be separated into a number of identical copies. Since the (nonrelativistic) Schrödinger equation conserves ∫ψ^*(x̅ )ψ(x̅ )d³x, this separation is such that repeated measurements will give coordinates with a distribution proportional to ψ^*(x̅ )ψ(x̅ ).